Scala analysis: xen18-erlich-pajara-10
2L 8s MOS for Pajara, L=172.17, s=106.57
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 106.570 cents 106.570000 2: 213.140 cents 213.140000 3: 385.310 cents 385.310000 4: 491.880 cents 491.880000 5: 598.450 cents 598.450000 6: 705.020 cents 705.020000 7: 811.590 cents 811.590000 8: 983.760 cents 983.760000 9: 1090.330 cents 1090.330000 10: 1196.900 cents 1196.900000
SHOW/INTERVAL
0: 106.5700 cents 106.5700 1: 106.5700 cents 106.5700 2: 106.5700 cents 106.5700 3: 172.1700 cents 172.1700 4: 106.5700 cents 106.5700 5: 106.5700 cents 106.5700 6: 106.5700 cents 106.5700 7: 106.5700 cents 106.5700 8: 172.1700 cents 172.1700 9: 106.5700 cents 106.5700 10: 106.5700 cents 106.5700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 106.57000 cents 1: 2 172.17000 cents 2: 6 213.14000 cents 2: 4 278.74000 cents 3: 4 319.71000 cents 3: 6 385.31000 cents 4: 2 426.28000 cents 4: 8 491.88000 cents 5: 10 598.45000 cents 6: 8 705.02000 cents 6: 2 770.62000 cents 7: 6 811.59000 cents 7: 4 877.19000 cents 8: 4 918.16000 cents 8: 6 983.76000 cents 9: 2 1024.73000 cents 9: 8 1090.33000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.88889 = 17/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 106.6 213.1 385.3 491.9 598.4 705.0 811.6 983.8 1090.3 1196.9 106.6 : 106.6 278.7 385.3 491.9 598.4 705.0 877.2 983.8 1090.3 1196.9 213.1 : 172.2 278.7 385.3 491.9 598.4 770.6 877.2 983.8 1090.3 1196.9 385.3 : 106.6 213.1 319.7 426.3 598.4 705.0 811.6 918.2 1024.7 1196.9 491.9 : 106.6 213.1 319.7 491.9 598.4 705.0 811.6 918.2 1090.3 1196.9 598.4 : 106.6 213.1 385.3 491.9 598.4 705.0 811.6 983.8 1090.3 1196.9 705.0 : 106.6 278.7 385.3 491.9 598.4 705.0 877.2 983.8 1090.3 1196.9 811.6 : 172.2 278.7 385.3 491.9 598.5 770.6 877.2 983.8 1090.3 1196.9 983.8 : 106.6 213.1 319.7 426.3 598.4 705.0 811.6 918.2 1024.7 1196.9 1090.3: 106.6 213.1 319.7 491.9 598.5 705.0 811.6 918.2 1090.3 1196.9 1196.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 106.5700 .. 172.1700 cents 65.60000 cents 106.57000 cents 2: 213.1400 .. 278.7400 cents 65.60000 cents 40.97000 cents 3: 319.7100 .. 385.3100 cents 65.60000 cents 40.97000 cents 4: 426.2800 .. 491.8800 cents 65.60000 cents 40.97000 cents 5: 598.4500 .. 598.4500 cents 1/1, 0.0000 cents 106.57000 cents 6: 705.0200 .. 770.6200 cents 65.60000 cents 106.57000 cents 7: 811.5900 .. 877.1900 cents 65.60000 cents 40.97000 cents 8: 918.1600 .. 983.7600 cents 65.60000 cents 40.97000 cents 9: 1024.7300 .. 1090.3300 cents 65.60000 cents 40.97000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 106.57000 cents, class 1 Average step (divided formal octave): 119.6900 cents Largest one step interval : 172.17000 cents Average / Smallest step : 1.123112 Largest / Average step : 1.438466 Largest / Smallest step : 1.615558 Median interval of one step : 106.57000 cents, amount: 8 Most common interval of one step : 106.57000 cents, amount: 8 Least squares average step : 120.03078 cents, oct.: 1200.30779 cents Scale is strictly proper Scale has 2 repeating blocks of 5 notes Blocks have Myhill's property chromas: 65.60000 cents and 40.97000 cents, ratio: 1.601172 generators: 1 of 106.57000 cents and 4 of 491.88000 cents ET pair of linear temperament : 22&34 Scale is maximally even for L / S <= 2 Scale is distributional even Step pattern alph. order: AABAAAABAA Step pattern size order : SSLSSSSLSS Scale is a Constant Structure, by a margin of 40.97000 cents Scale diversity : 1.205375 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.561534 Rothenberg efficiency (ambiguous key): 0.513333 redundancy: 0.486667 Efficiency x scale size : 5.133333 Number of different interval sizes : 17 = 1.88889 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.88889 = 17/9 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 40.97000 cents Most common intervals : 598.45000 cents & inv., amount: 10 Number of recognisable fifths : 8, average 705.0200 cents Number of recognisable fourths : 8, average 491.8800 cents Scale contains two identical disjunct pentachords Formal octave complements present : 10 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 5 Limited inverse transpositions : 5 Inversional symmetry on degrees : 0 5 Inversional symmetry on intervals : 2-3 7-8 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.5545 c. M:-26.2400 c. 12: 1 1 2 1 1 1 1 2 1 1 P B ME I SD: 9.6567 c. M:-13.6567 c. Symmetrical Decatonic 22: 2 2 3 2 2 2 2 3 2 2 SP B ME I SD: 3.1666 c. M:-4.4782 c. Static Symmetrical Major 34: 3 3 5 3 3 3 3 5 3 3 SP B DE I SD: 1.3593 c. M:-1.9224 c. 56: 5 5 8 5 5 5 5 8 5 5 SP B DE I SD: 0.4187 c. M:-0.5921 c. 90: 8 8 13 8 8 8 8 13 8 8 SP B DE I SD: 0.2530 c. M:-0.3578 c. 146: 13 13 21 13 13 13 13 21 13 13 SP B DE I SD: 0.0046 c. M:-0.0066 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 3.1000 cents 2 x x x x x 3 x x x 4 S SD: 2.1797 cents 3 x x x 4 x x 5 x x 6 S SD: 24.3651 cents 4 x x 5 x x 6 x 7 x 8 S SD: 3.8974 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 15.8324 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 16.5979 cents 7 x 8:9 x 10 x 11:12:13:14 S SD: 11.8940 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 7.2794 cents 9 x 10:11:12:13 x 14:16:17:18 S SD: 9.9459 cents 10 x 11 x 13:14:15:16:18:19:20 SD: 9.3488 cents 11:12 x 14:15:16:17:18:19:21:22 SD: 13.0751 cents 12:13:14:15:16:17:18:19:21:23:24 SD: 7.5929 cents 15:16:17:19:20:21:23:24:26:28:30 SD: 5.6832 cents 16:17:18:20:21:23:24:26:28:30:32 SD: 5.0071 cents 22:23:25:27:29:31:33:35:39:41:44 SD: 4.8893 cents 24:26:27:30:32:34:36:38:42:45:48 SD: 4.0895 cents 28:30:32:35:37:40:42:45:49:53:56 SD: 3.8550 cents 29:31:33:36:39:41:44:46:51:54:58 SD: 3.8052 cents 30:32:34:37:40:42:45:48:53:56:60 SD: 3.0769 cents 31:33:35:39:41:44:47:50:55:58:62 SD: 2.9972 cents 32:34:36:40:43:45:48:51:56:60:64 SD: 2.8466 cents 40:43:45:50:53:57:60:64:71:75:80 SD: 2.8140 cents 43:46:49:54:57:61:65:69:76:81:86 SD: 2.4995 cents 44:47:50:55:58:62:66:70:78:83:88 SD: 2.3204 cents 46:49:52:57:61:65:69:74:81:86:92 SD: 2.0914 cents 48:51:54:60:64:68:72:77:85:90:96 SD: 1.5658 cents 60:64:68:75:80:85:90:96:106:113:120 SD: 1.2492 cents 76:81:86:95:101:107:114:121:134:143:152 SD: 1.1624 cents 77:82:87:96:102:109:116:123:136:145:154 SD: 1.0837 cents 92:98:104:115:122:130:138:147:162:173:184 SD: 0.8119 cents 97:103:110:121:129:137:146:155:171:182:194 SD: 0.7864 cents 107:114:121:134:142:151:161:171:189:201:214 SD: 0.7341 cents 124:132:140:155:165:175:186:198:219:233:248 SD: 0.6991 cents 137:146:155:171:182:194:206:219:242:257:274 SD: 0.6648 cents 145:154:164:181:193:205:218:232:256:272:289 SD: 0.5805 cents 174:185:197:217:231:246:261:278:307:327:347 SD: 0.5696 cents 177:188:200:221:235:250:266:283:312:332:353 SD: 0.4690 cents 189:201:214:236:251:267:284:302:334:355:377 SD: 0.3496 cents 221:235:250:276:294:312:332:353:390:415:441 SD: 0.3115 cents 237:252:268:296:315:335:356:379:418:445:473 SD: 0.2368 cents 298:317:337:372:396:421:448:476:526:559:595 SD: 0.2272 cents 344:366:389:430:457:486:517:550:607:646:687 SD: 0.1900 cents 426:453:482:532:566:602:640:681:752:800:850 SD: 0.1661 cents 472:502:534:590:627:667:709:754:833:886:942 SD: 0.1637 cents 489:520:553:611:650:691:735:781:863:918:976 SD: 0.1562 cents 490:521:554:612:651:692:736:783:865:920:978 SD: 0.1497 cents 533:567:603:666:708:753:801:852:941:1001:1064 SD: 0.1308 cents